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Structure Determination of Organic Compounds - Tables of Spectral Data

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While modern techniques of nuclear magnetic resonance copy and mass spectrometry have changed the ways of data acquisition and greatly extended the capabilities of these methods, the bas

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Ern¨o Pretsch · Philippe B¨uhlmann ·

Martin Badertscher

Structure Determination

of Organic Compounds Tables of Spectral Data

Fourth, Revised and Enlarged Edition

123

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Institute of Biogeochemistry and

 Springer-Verlag Berlin Heidelberg 2009

This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication

or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,

1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law.

The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cover design: WMXDesign GmbH

Printed on acid-free paper

9 8 7 6 5 4 3 2 1

springer.com

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The ongoing success of the earlier versions of this book motivated us to prepare

a new edition While modern techniques of nuclear magnetic resonance copy and mass spectrometry have changed the ways of data acquisition and greatly extended the capabilities of these methods, the basic parameters, such as chemical shifts, coupling constants, and fragmentation pathways remain the same However, since the amount and quality of available data has considerably increased over the years, we decided to prepare a significantly revised manuscript It follows the same basic concepts, i.e., it provides a representative, albeit limited set of reference data for the interpretation of 13C NMR, 1H NMR, IR, mass, and UV/Vis spectra We also added a new chapter with reference data for 19F and 31P NMR spectroscopy and, in the chapter on infrared spectroscopy, we newly refer to important Raman bands Since operating systems of computers become outdated much faster than printed media, we decided against providing a compact disk with this new edition The limited versions of the NMR spectra estimation programs can be downloaded from the home page of the developing company (www.upstream.ch/support/book_down-loads.html)

spectros-We thank numerous colleagues who helped us in many different ways to plete the manuscript We are particularly indebted to Dr Dorothée Wegmann for her expertise with which she eliminated many errors and inconsistencies of the earlier versions Special thanks are due to Prof Wolfgang Robien for providing us with reference data from his outstanding 13C NMR database, CSEARCH Another high-quality source of information was the Spectral Database System of the National Institute of Advanced Industrial Science and Technology (http://riodb01.ibase.aist.go.jp/sdbs/), Tsukuba, Ibaraki (Japan)

com-In spite of great efforts and many checks to eliminate errors, it is likely that some mistakes or inconsistencies remain We would like to encourage our readers to con-tact us with comments and suggestions under one of the following addresses: Prof Ernö Pretsch, Institute of Biogeochemistry and Pollutant Dynamics, ETH Zürich, CH-8092 Zürich, Switzerland, e-mail: pretsche@ethz.ch, Prof Philippe Bühlmann, Department of Chemistry, University of Minnesota, 207 Pleasant St SE, Minne-apolis, MN 55455, USA, e-mail: buhlmann@umn.edu, or Dr Martin Badertscher, Laboratory of Organic Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland, e-mail: badertscher@org.chem.ethz.ch

Zürich and Minneapolis, November 2008

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1 Introduction 1

1.1 Scope and Organization 1

1.2 Abbreviations and Symbols 3

2 Summary Tables 5

2.1 General Tables 5

2.1.1 Calculation of the Number of Double Bond Equivalents from the Molecular Formula 5

2.1.2 Properties of Selected Nuclei 6

2.2 13C NMR Spectroscopy 7

2.3 1H NMR Spectroscopy 10

2.4 IR Spectroscopy 13

2.5 Mass Spectrometry 18

2.5.1 Average Masses of Naturally Occurring Elements with Masses and Representative Relative Abundances of Isotopes 18

2.5.2 Ranges of Natural Isotope Abundances of Selected Elements 25 2.5.3 Isotope Patterns of Naturally Occurring Elements 26

2.5.4 Calculation of Isotope Distributions 27

2.5.5 Isotopic Abundances of Various Combinations of Chlorine, Bromine, Sulfur, and Silicon 29

2.5.6 Isotope Patterns of Combinations of Cl and Br 31

2.5.7 Indicators of the Presence of Heteroatoms 32

2.5.8 Rules for Determining the Relative Molecular Weight (Mr) 34 2.5.9 Homologous Mass Series as Indications of Structural Type 35 2.5.10 Mass Correlation Table 37

2.5.11 References 45

2.6 UV/Vis Spectroscopy 46

3 Combination Tables 49

3.1 Alkanes, Cycloalkanes 49

3.2 Alkenes, Cycloalkenes 50

3.3 Alkynes 51

Contents

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VIII Contents

3.4 Aromatic Hydrocarbons 52

3.5 Heteroaromatic Compounds 53

3.6 Halogen Compounds 54

3.7 Oxygen Compounds 56

3.7.1 Alcohols and Phenols 56

3.7.2 Ethers 57

3.8 Nitrogen Compounds 59

3.8.1 Amines 59

3.8.2 Nitro Compounds 60

3.9 Thiols and Sulfides 61

3.10 Carbonyl Compounds 62

3.10.1 Aldehydes 62

3.10.2 Ketones 63

3.10.3 Carboxylic Acids 64

3.10.4 Esters and Lactones 65

3.10.5 Amides and Lactams 67

4 13 C NMR Spectroscopy 69

4.1 Alkanes 69

4.1.1 Chemical Shifts 69

4.1.2 Coupling Constants 78

4.1.3 References 79

4.2 Alkenes 80

4.2.1 Chemical Shifts 80

4.2.2 Coupling Constants 84

4.2.3 References 84

4.3 Alkynes 85

4.3.1 Chemical Shifts 85

4.3.2 Coupling Constants 85

4.3.3 References 86

4.4 Alicyclics 87

4.4.1 Chemical Shifts 87

4.4.2 Coupling Constants 92

4.5 Aromatic Hydrocarbons 93

4.5.1 Chemical Shifts 93

4.5.2 Coupling Constants 100

4.5.3 References 100

4.6 Heteroaromatic Compounds 101

4.6.1 Chemical Shifts 101

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4.6.2 Coupling Constants 108

4.7 Halogen Compounds 109

4.7.1 Fluoro Compounds 109

4.7.2 Chloro Compounds 111

4.7.3 Bromo Compounds 112

4.7.4 Iodo Compounds 113

4.7.5 References 113

4.8 Alcohols, Ethers, and Related Compounds 114

4.8.1 Alcohols 114

4.8.2 Ethers 115

4.9 Nitrogen Compounds 117

4.9.1 Amines 117

4.9.2 Nitro and Nitroso Compounds 119

4.9.3 Nitrosamines and Nitramines 120

4.9.4 Azo and Azoxy Compounds 120

4.9.5 Imines and Oximes 120

4.9.6 Hydrazones and Carbodiimides 121

4.9.7 Nitriles and Isonitriles 122

4.9.8 Isocyanates, Thiocyanates, and Isothiocyanates 122

4.10 Sulfur Compounds 123

4.10.1 Thiols 123

4.10.2 Sulfides 123

4.10.3 Disulfides and Sulfonium Salts 124

4.10.4 Sulfoxides and Sulfones 125

4.10.5 Sulfonic and Sulfinic Acids and Derivatives 126

4.10.6 Sulfurous and Sulfuric Acid Derivatives 126

4.10.7 Sulfur-Containing Carbonyl Derivatives 127

4.11 Carbonyl Compounds 128

4.11.1 Aldehydes 128

4.11.2 Ketones 129

4.11.3 Carboxylic Acids 131

4.11.4 Esters and Lactones 133

4.11.5 Amides and Lactams 135

4.11.6 Miscellaneous Carbonyl Derivatives 137

4.12 Miscellaneous Compounds 139

4.12.1 Compounds with Group IV Elements 139

4.12.2 Phosphorus Compounds 140

4.12.3 Miscellaneous Organometallic Compounds 142

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X Contents

4.13 Natural Products 144

4.13.1 Amino Acids 144

4.13.2 Carbohydrates 148

4.13.3 Nucleotides and Nucleosides 150

4.13.4 Steroids 152

4.14 Spectra of Solvents and Reference Compounds 153

4.14.1 13C NMR Spectra of Common Deuterated Solvents 153

4.14.2 13C NMR Spectra of Secondary Reference Compounds 155

4.14.3 13C NMR Spectrum of a Mixture of Common Nondeuterated Solvents 156

5 1 H NMR Spectroscopy 157

5.1 Alkanes 157

5.1.1 Chemical Shifts 157

5.1.2 Coupling Constants 162

5.2 Alkenes 164

5.2.1 Substituted Ethylenes 164

5.2.2 Conjugated Dienes 170

5.2.3 Allenes 171

5.3 Alkynes 172

5.4 Alicyclics 173

5.5 Aromatic Hydrocarbons 177

5.6 Heteroaromatic Compounds 184

5.6.1 Non-Condensed Heteroaromatic Rings 184

5.6.2 Condensed Heteroaromatic Rings 191

5.7 Halogen Compounds 196

5.7.1 Fluoro Compounds 196

5.7.2 Chloro Compounds 197

5.7.3 Bromo Compounds 198

5.7.4 Iodo Compounds 199

5.8 Alcohols, Ethers, and Related Compounds 200

5.8.1 Alcohols 200

5.8.2 Ethers 202

5.9 Nitrogen Compounds 205

5.9.1 Amines 205

5.9.2 Nitro and Nitroso Compounds 207

5.9.3 Nitrites and Nitrates 208

5.9.4 Nitrosamines, Azo and Azoxy Compounds 208

5.9.5 Imines, Oximes, Hydrazones, and Azines 209

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5.9.6 Nitriles and Isonitriles 210

5.9.7 Cyanates, Isocyanates, Thiocyanates, and Isothiocyanates 211

5.10 Sulfur Compounds 212

5.10.1 Thiols 212

5.10.2 Sulfides 213

5.10.3 Disulfides and Sulfonium Salts 214

5.10.4 Sulfoxides and Sulfones 214

5.10.5 Sulfonic, Sulfurous, and Sulfuric Acids and Derivatives 215

5.10.6 Thiocarboxylate Derivatives 215

5.11 Carbonyl Compounds 216

5.11.1 Aldehydes 216

5.11.2 Ketones 217

5.11.3 Carboxylic Acids and Carboxylates 218

5.11.4 Esters and Lactones 219

5.11.5 Amides and Lactams 220

5.11.6 Miscellaneous Carbonyl Derivatives 224

5.12 Miscellaneous Compounds 226

5.12.1 Compounds with Group IV Elements 226

5.12.2 Phosphorus Compounds 227

5.12.3 Miscellaneous Compounds 230

5.12.4 References 231

5.13 Natural Products 232

5.13.1 Amino Acids 232

5.13.2 Carbohydrates 235

5.13.3 Nucleotides and Nucleosides 237

5.14 Spectra of Solvents and Reference Compounds 239

5.14.1 1H NMR Spectra of Common Deuterated Solvents 239

5.14.2 1H NMR Spectra of Secondary Reference Compounds 241

5.14.3 1H NMR Spectrum of a Mixture of Common Nondeuterated Solvents 242

6 Heteronuclear NMR Spectroscopy 243

6.1 19F NMR Spectroscopy 243

6.1.1 19F Chemical Shifts of Perfluoroalkanes 243

6.1.2 Estimation of 19F Chemical Shifts of Substituted Fluoroethylenes 247

6.1.3 Coupling Constants in Fluorinated Alkanes and Alkenes 248

6.1.4 19F Chemical Shifts of Allenes and Alkynes 249

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XII Contents

6.1.5 19F Chemical Shifts and Coupling Constants of Fluorinated

Alicyclics 250

6.1.6 19F Chemical Shifts and Coupling Constants of Aromatics and Heteroaromatics 251

6.1.7 19F Chemical Shifts of Alcohols and Ethers 254

6.1.8 19F Chemical Shifts of Fluorinated Amine, Imine, and Hydroxyl amine Derivatives 255

6.1.9 19F Chemical Shifts of Sulfur Compounds 256

6.1.10 19F Chemical Shifts of Carbonyl and Thiocarbonyl Compounds 257

6.1.11 19F Chemical Shifts of Fluorinated Boron, Phosphorus, and Silicon Compounds 258

6.1.12 19F Chemical Shifts of Natural Product Analogues 259

6.1.13 References 260

6.2 31P NMR Spectroscopy 261

6.2.1 31P Chemical Shifts of Tricoordinated Phosphorus, PR1R2R3 261 6.2.2 31P Chemical Shifts of Tetracoordinated Phosphonium Compounds 262

6.2.3 31P Chemical Shifts of Compounds with a P=C or P=N Bond 263 6.2.4 31P Chemical Shifts of Tetracoordinated P(=O) and P(=S) Compounds 264

6.2.5 31P Chemical Shifts of Penta- and Hexacoordinated Phosphorus Compounds 266

6.2.6 31P Chemical Shifts of Natural Phosphorus Compounds 267

7 IR Spectroscopy 269

7.1 Alkanes 269

7.2 Alkenes 272

7.2.1 Monoenes 272

7.2.2 Allenes 275

7.3 Alkynes 276

7.4 Alicyclics 277

7.5 Aromatic Hydrocarbons 279

7.6 Heteroaromatic Compounds 282

7.7 Halogen Compounds 284

7.7.1 Fluoro Compounds 284

7.7.2 Chloro Compounds 285

7.7.3 Bromo Compounds 286

7.7.4 Iodo Compounds 286

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7.8 Alcohols, Ethers, and Related Compounds 287

7.8.1 Alcohols and Phenols 287

7.8.2 Ethers, Acetals, and Ketals 288

7.8.3 Epoxides 290

7.8.4 Peroxides and Hydroperoxides 291

7.9 Nitrogen Compounds 292

7.9.1 Amines and Related Compounds 292

7.9.2 Nitro and Nitroso Compounds 294

7.9.3 Imines and Oximes 296

7.9.4 Azo, Azoxy, and Azothio Compounds 298

7.9.5 Nitriles and Isonitriles 299

7.9.6 Diazo Compounds 300

7.9.7 Cyanates and Isocyanates 301

7.9.8 Thiocyanates and Isothiocyanates 302

7.10 Sulfur Compounds 304

7.10.1 Thiols and Sulfides 304

7.10.2 Sulfoxides and Sulfones 305

7.10.3 Thiocarbonyl Derivatives 307

7.10.4 Thiocarbonic Acid Derivatives 307

7.11 Carbonyl Compounds 310

7.11.1 Aldehydes 310

7.11.2 Ketones 311

7.11.3 Carboxylic Acids 314

7.11.4 Esters and Lactones 316

7.11.5 Amides and Lactams 319

7.11.6 Acid Anhydrides 322

7.11.7 Acid Halides 323

7.11.8 Carbonic Acid Derivatives 324

7.12 Miscellaneous Compounds 327

7.12.1 Silicon Compounds 327

7.12.2 Phosphorus Compounds 328

7.12.3 Boron Compounds 331

7.13 Amino Acids 332

7.14 Solvents, Suspension Media, and Interferences 333

7.14.1 Infrared Spectra of Common Solvents 333

7.14.2 Infrared Spectra of Suspension Media 334

7.14.3 Interferences in Infrared Spectra 335

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XIV Contents

8 Mass Spectrometry 337

8.1 Alkanes 337

8.2 Alkenes 339

8.3 Alkynes 341

8.4 Alicyclics 342

8.5 Aromatic Hydrocarbons 345

8.6 Heteroaromatic Compounds 347

8.7 Halogen Compounds 352

8.8 Alcohols, Ethers, and Related Compounds 354

8.8.1 Alcohols and Phenols 354

8.8.2 Hydroperoxides 356

8.8.3 Ethers 356

8.8.4 Aliphatic Epoxides 359

8.8.5 Aliphatic Peroxides 360

8.8.6 References 361

8.9 Nitrogen Compounds 362

8.9.1 Amines 362

8.9.2 Nitro Compounds 364

8.9.3 Diazo Compounds and Azobenzenes 364

8.9.4 Azides 365

8.9.5 Nitriles and Isonitriles 366

8.9.6 Cyanates, Isocyanates, Thiocyanates, and Isothiocyanates 367

8.9.7 References 369

8.10 Sulfur Compounds 371

8.10.1 Thiols 371

8.10.2 Sulfides and Disulfides 371

8.10.3 Sulfoxides and Sulfones 373

8.10.4 Sulfonic Acids and Their Esters and Amides 376

8.10.5 Thiocarboxylic Acid Esters 377

8.10.6 References 378

8.11 Carbonyl Compounds 379

8.11.1 Aldehydes 379

8.11.2 Ketones 380

8.11.3 Carboxylic Acids 381

8.11.4 Carboxylic Acid Anhydrides 382

8.11.5 Esters and Lactones 382

8.11.6 Amides and Lactams 384

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8.11.7 Imides 386

8.11.8 References 387

8.12 Miscellaneous Compounds 388

8.12.1 Trialkylsilyl Ethers 388

8.12.2 Phosphorus Compounds 388

8.12.3 References 389

8.13 Mass Spectra of Common Solvents and Matrix Compounds 390

8.13.1 Electron Impact Ionization Mass Spectra of Common Solvents 390

8.13.2 Spectra of Common FAB MS Matrix and Calibration Compounds 393

8.13.3 Spectra of Common MALDI MS Matrix Compounds 398

8.13.4 References 400

9 UV/Vis Spectroscopy 401

9.1 Correlation between Wavelength of Absorbed Radiation and Observed Color 401

9.2 Simple Chromophores 401

9.3 Conjugated Alkenes 403

9.3.1 Dienes and Polyenes 403

9.3.2 α,β-Unsaturated Carbonyl Compounds 404

9.4 Aromatic Hydrocarbons 406

9.4.1 Monosubstituted Benzenes 406

9.4.2 Polysubstituted Benzenes 407

9.4.3 Aromatic Carbonyl Compounds 408

9.5 Reference Spectra 409

9.5.1 Alkenes and Alkynes 409

9.5.2 Aromatic Compounds 410

9.5.3 Heteroaromatic Compounds 415

9.5.4 Miscellaneous Compounds 417

9.5.5 Nucleotides 419

9.6 Common Solvents 420

Subject Index 421

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1 Introduction

1.1 Scope and Organization

The present data collection is intended to serve as an aid in the interpretation of molecular spectra for the elucidation and confirmation of the structure of organic compounds It consists of reference data, spectra, and empirical correlations from

1H, 13C, 19F, and 31P nuclear magnetic resonance (NMR), infrared (IR), mass, and ultraviolet–visible (UV/Vis) spectroscopy It is to be viewed as a supplement to textbooks and specific reference works dealing with these spectroscopic techniques The use of this book to interpret spectra only requires the knowledge of basic prin-ciples of the techniques, but its content is structured in a way that it will serve as a reference book also to specialists

Chapters 2 and 3 contain Summary Tables and Combined Tables of the most relevant spectral characteristics of structural elements While Chapter 2 is orga-nized according to the different spectroscopic methods, Chapter 3 for each class

of structural elements supplies spectroscopic information obtained with various techniques These two chapters should assist users less familiar with spectra inter-pretation to identify the classes of structural elements present in samples of their interest The four chapters with data from 13C NMR, 1H NMR, IR spectroscopy, and mass spectrometry are ordered in the same manner by compound types These cover the various carbon skeletons (alkyl, alkenyl, alkynyl, alicyclic, aromatic, and heteroaromatic), the most important substituents (halogen, single-bonded oxygen, nitrogen, sulfur, and carbonyl), and some specific compound classes (miscellaneous compounds and natural products) Finally, a spectra collection of common solvents, auxiliary compounds (such as matrix materials and references), and commonly found impurities is provided with each method Not only the strictly analogous order of the data but also the optical marks on the edge of the pages help fast cross-referencing between the various spectroscopic techniques Because their data sets are less comprehensive, the chapters on 19F and 31P NMR and UV/Vis are organized somewhat differently Although currently UV/Vis spectroscopy is only marginally relevant to structure elucidation, its importance might increase by the advent of high-throughput analyses Also, the reference data presented in the UV/Vis chapter are useful in connection with optical sensors and the widely applied UV/Vis detec-tors in chromatography and electrophoresis

Since a great part of the tabulated data either comes from our own measurements

or is based on a large body of literature data, comprehensive references to published sources are not included Whenever possible, the data refer to conventional modes and conditions of measurement For example, unless the solvent is indicated, the NMR chemical shifts were normally determined with deuterochloroform Likewise, the IR spectra were measured using solvents of low polarity, such as chloroform or

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carbon disulfide Mass spectral data were recorded with electron impact ionization

at 70 eV

While retaining the basic structure of the previous editions, numerous reference entries have been updated and new entries have been added Altogether, about 20%

of the data is new The chapter on 19F and 31P NMR is entirely new, and the section

on IR spectroscopy now includes references to important Raman bands

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1.2 Abbreviations and Symbols 3

1.2 Abbreviations and Symbols

M+. molecular radical ion

m/z mass to charge ratio

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2.1 General Tables

2.1.1 Calculation of the Number of Double Bond Equivalents from the Molecular Formula

General Equation

double bond equivalents = 1 + ½ ∑ ni i (vi – 2)

ni: number of atoms of element i in molecular formula

vi: formal valence of element i

Short Cut

For compounds containing only C, H, O, N, S, and halogens, the following steps permit a quick and simple calculation of the number of double bond equivalents:

1 O and divalent S are deleted from the molecular formula

2 Halogens are replaced by hydrogen

3 Trivalent N is replaced by CH

4 The resulting hydrocarbon, CnHx, is compared with the saturated bon, CnH2n+2 Each double bond equivalent reduces the number of hydrogen atoms by 2:

hydrocar-double bond equivalents = ½ (2 n + 2 – x)

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Frequency [MHz] at 2.35 Tesla

Relative sensitivity

of nucleus

Relative sensitivity

at natural abundance

Electricquadrupole moment [e × 10-24

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2.2 13 C NMR Spectroscopy 7

–C

2.2 13C NMR Spectroscopy

Summary of the Regions of Chemical Shifts, δ (in ppm), for Carbon Atoms in

Various Chemical Environments (carbon atoms are specified as follows: Q for

CH3, T for CH2, D for CH, and S for C)

C

140 120 100 80 60 40 20 0 ppm

180 160

Q Q T T D Q D,S Q D Q S T D S T

C

140 120 100 80 60 40 20 0 ppm

180 160 200

220 240

T D S Q S

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140 120 100 80 60 40 20 0 ppm

180 160 200

220 240

D, S

T, D, S S

D, S S

D, S

D, S S S

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13 C Chemical Shifts of Carbonyl Groups (δ in ppm)

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10 2 Summary Tables

2.3 1H NMR Spectroscopy

Summary of the Regions of Chemical Shifts, δ (in ppm), for Hydrogen Atoms

in Various Chemical Environments

0 ppm 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 ppm 1 2 3 4 5 6 7 8 9 10 11 12 13 14

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0 ppm 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 ppm 1 2 3 4 5 6 7 8 9 10 11 12 13 14

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12 2 Summary Tables

0 ppm 1 2 3 4 5 6 7 8 9 10 11 12 13 14

O H N O H O

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2.4 IR Spectroscopy

Summary of the Most Important IR Absorption Bands ( ~ν in cm -1 )

δ

2000 1500 1000 500 cm 2500

3000

2000 1500 1000 500 cm 2500

3000

δ

δ

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14 2 Summary Tables

Summary of IR Absorption Bands of Carbonyl Groups ( ~ν in cm -1 )

1550 cm 1600

1650 1700 1750 1800 1850

1550 cm 1600

1650 1700 1750 1800 1850

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1550 cm 1600

1650 1700 1750 1800 1850

1550 cm 1600

1650 1700 1750 1800 1850

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16 2 Summary Tables

1550 cm 1600

1650 1700 1750 1800 1850

1550 cm 1600

1650 1700 1750 1800 1850

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1550 cm 1600

1650 1700 1750 1800 1850

1550 cm 1600

1650 1700 1750 1800 1850

(in solution)

(solid)

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a Natural variations in the isotopic composition of terrestrial materials do not allow

to give a more precise value

b The mole ratio of 2H in hydrogen from gas cylinders was reported to be as low as 0.000032

c Commercially available materials may have substantially different isotopic compositions if they were subjected to undisclosed or inadvertent isotopic fractionation

d Materials depleted in 6Li are commercial sources of laboratory shelf reagents and are known to have 6Li abundances in the range of 2.0007–7.672 atom percent, with natural materials at the higher end of this range Average atomic masses vary between 6.939 and 6.996; if a more accurate value is required, it must be determined for the specific material

e Materials depleted in 235U are commercial sources of laboratory shelf reagents

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2.5.2 Ranges of Natural Isotope Abundances of Selected Elements [3] Element Range

Isotope [atom %] Element Isotope [atom %]Range Element Isotope [atom %]Range

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26 2 Summary Tables

2.5.3 Isotope Patterns of Naturally Occurring Elements

The mass of the most abundant isotope is given under the symbol of the element The lightest isotope is shown at the left end of the x axis

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2.5.4 Calculation of Isotope Distributions

The characteristic abundance patterns resulting from the combination of more than one polyisotopic element can be calculated from the relative abundances

of the different isotopes The following polynomial expression gives the isotope distribution of a polyisotopic molecule:

{pi1 Α0 + pi2 Α(mi2 - mi1) + pi3 Α(mi3 - mi1) + …}ni ×

{pj1 Α0 + pj2 Α(mj2 - mj1) + pj3 Α(mj3 - mj1) + …}nj × {…

where pix is the relative abundance of the xth isotope of element i, mix is the mass of

the xth isotope of the element i, and the exponent ni stands for the number of atoms

of the element i in the molecule The expansion of this polynomial expression after

inserting the pix and mix values for all the isotopes 1, 2, 3, … of the elements i, j, …

of a given molecule yields an expression that represents the isotope distribution:

w0 Α0 + w r Αr + w s Αs + w t Αt + …

where the values of w0, w r , w s , w t, … are the relative abundances of M+·, [M + r]+·,

[M + s]+·, [M + t]+·,… , respectively The use of Α(mix - mi1) allows to determine the

values of r, s, t,… simply by expanding the general polynomial A numerical value

for A, which has no intrinsic meaning, is never needed

For example, for CBr2Cl2, the above equation gives rise to the following expression:

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2H on isotope patterns is usually insignificant Also, 13C is often negligible when focussing on peaks of the series [M+2n]+·, which then results in patterns that are characteristic for halogens, sulfur, and silicon In large molecules, however, iso-topes of low abundance cannot be neglected For example, in the case of buckmin-ster fullerene (C60), not only M+· (relative intensity, 100%) and [M+1]+· (64.80%), but also [M+2]+· (20.65%), [M+3]+· (4.31%), and even [M+4]+· (0.66%) are quite significant ions.

With the above algorithm, typical isotope patterns can be readily calculated ually by applying the general equation and neglecting isotopes of low abundance The outlined procedure can also be easily implemented and evaluated with generic computer software that allows simple calculations Dedicated and user-friendly pro-grams that already contain the necessary isotope abundances and masses are avail-able Incidentally, because the use of the above equation for systems with 1000 or more polyisotopic atoms results in excessive calculation times, more efficient but somewhat more complicated algorithms have been developed for implementation in dedicated programs [4] Typical isotope patterns are given on the following pages

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